Karl Pearson and Egon S. Pearson 
147 
We shall proceed to calculate X^s' three values of r which lie near the 
probable value of r as found from each column. We will take these as •45, '50 and 
•55 ; from these values we shall obtain h.^. for each column from (xiv) and inter- 
polating the real between them find the corresponding columnar r, which will 
be then substituted in (xv) by aid of Table X to obtain the columnar mean kg.. 
Table XI gives the values of X.^,,' for r — "45, '50 and '55, and Table XII the 
resulting values of kg. 
TABLE XT. Values of for r = -45, -50 arid -55. 
s' 
r 
s = l 
s = 2 
s = 3 
s = 4 
S — O 
s = 6 
s = 7 
1 
(a) 
(b) 
- •014,742,01 
-•017,038,00 
-■020,616,58 
- -021,5.54,08 
-•000,400,18 
--000,383,88 
— UUW,oOD,'±U 
+ •000,974,70 
+ •OOO, 731,59 
1 -nnn i u 
■f- uuu,oio,yo 
+ -000,377,97 
+ -000,258,31 
+ -000,168,60 
+ ^000,409,54 
+ •000,246,06 
+ ^000,044,95 
+ •000,015,95 
•Ann nnQ oo 
— uuu,uuo,iiy 
2 
(a) 
(b) 
(a) 
(b) 
(c) 
- •043,836,23 
-•045,046,53 
— '045 86C) 07 
- -133,792,74 
-■140,080,50 
— ■^ 4fi 85C» 94 
- •003,545,25 
-■003,775,08 
- -OOd 0-?fi Q8 
+ •021,169,83 
+ ^019,705,30 
-^-•018 OQO 5'^ 
+ -010,795,76 
+ -009,504,62 
+ "008 1 50 14 
+ •015,963,45 
+ •012,993,41 
4- -01 0 1 41 'iO 
+ •003,2.58,21 
+ ^002,268,84 
3 
- -014,665,26 
- -012,764,50 
--010,711,23 
- ^082,820,10 
- ■082,030,73 
- ^080,956,49 
- -002,204,29 
- ■002,275,94 
-•002,360,54 
+ ■030,133,27 
+ ■030,479,17 
+ •030,869,67 
+ ■018,460,19 
+ -018,233,88 
+ -017,938,38 
+ -033,767,07 
+ •031,794,16 
+ -029,455,85 
+ •009,791,12 
+ •008,188,80 
+ •006,551,72 
4 
(a) 
(b) 
(0) 
- -003,450,60 
- -002,645,25 
- -001,920,26 
--028,237,21 
- -026,280,92 
--024,106,94 
- ^000,587,66 
- ^000,528,69 
- ^000,459,56 
+ •017,032,32 
+ ■017,630,94 
+ ■018,316,53 
+ -011,713,27 
+ ■012,084,98 
+ -012,492,17 
+ •024,762,-35 
+ ^024,998,89 
+ •025,139,70 
+ ^009,092,34 
+ -008,434,25 
+ -007,601,99 
5 
(a) 
(b) 
(c) 
- -001,562,59 
--001,096,19 
- -000,731,63 
- -016,357,80 
--014,410,34 
- -012,372,26 
-•000,196,08 
-•000,106,48 
- ^000,003,49 
+ 013,951,10 
+ ■014,492,89 
+ •015,100,01 
+ -010,408,16 
+ ■010,926,94 
+ •011,507,01 
+ ^024,456,57 
+ •025,583,17 
+ -026,761,82 
+ -010,780,30 
+ ■010,698,56 
+ -010,435,95 
6 
(«) 
ib) 
(c) 
- -000,728,92 
- -000,448,58 
- -000,255,73 
- -010,344,20 
- -008,432,81 
- -006,613,75 
+ -000,068,82 
+ •000,177,88 
+ -000,295,92 
+ ■013,421,77 
+ ■013,793,06 
+ ■014,164,31 
+ •011,082,88 
+ •011,705,64 
+ •012,382,26 
+ ■005,018,14 
+ •005,142,06 
+ •005,217,99 
+ -029,840,53 
+ •032,119,62 
+ •034,601,52 
+ ■016,766,62 
+ •017,871,20 
+ -018,889,99 
7 
(«) 
(b) 
(0) 
- -000,090,63 
--000,037,11 
- -000,000,75 
--002,150,92 
- -001,530,11 
- -001,037,56 
+ -000,121,52 
+ ■000,149,03 
+ -000,167,89 
+ •005,185,57 
+ -005,035,92 
+ -004,808,83 
+ •016,965,98 
+ •018,430,12 
+ •019,928,67 
+ •014,51.5,02 
+ •016,770,70 
+ •019,271,47 
TABLE XII. Values of h,. for Columns. 
r 1 s = l 
1 
s = 2 
s = 3 
s = 4 
ti = 5 
s = 6 
s = 7 
•45 
•50 
•55 
-2-19299 
-2-18505 
-2-17567 
- ^92114 
- ^91848 
- -91485 
- ^02549 
- ^02538 
- -02521 
+ -56650 
+ -56616 
+ -56580 
+ -98336 
+ -98315 
+ -98286 
+ 1-45054 
+ 1 ^44900 
+ 1-44685 
+ 2-30569 
+ 2-29880 
+ 2-28999 
Actual Aj. 
-2-19667 
-•91404 
- -02553 
+ -56594 
+ -98333 
+ 1 -44723 
+ 2-29464 
Extra- or 
Interpolated r 
•4229 
•5599 
-4167 
-5309 
-4585 
-5426 
-5249 
10—2 
